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Lunar puzzle that has clues but no answers

Of all tricks of the eye, the "moon illusion" - the apparent enlargement of the full moon when seen low over the horizon - is probably the most famous and also one of the most puzzling. Now, for the first time, we have a scholarly work devoted entirely to it. Both the authors are psychologists; they state that "the book has taken many years to write", and this is evident from the extensive quotations and references.

It is undeniable that the lower-down moon appears much larger than the moon at high altitude. It is equally undeniable that we are dealing with nothing more than illusion, because the apparent diameter of the lunar disc is unchanged - in fact, the low moon should be fractionally smaller, because the Earth is a rotating globe. So what is the cause of the illusion?

The illusion has been known for a very long time. For example, it was discussed in detail by the 2nd-century astronomer Ptolemy of Alexandria, last of the great scientists of classical times, and references to it go back much further than that. All sorts of explanations have been proposed. Ptolemy's was simple and ingenious. He pointed out that the low moon is seen against a foreground of terrestrial objects - trees, houses and so on - and this may be termed "filled space"; on the other hand, the high moon is seen against "empty space", with nothing between us and it, so that there are no available objects to act as comparisons. Yet the illusion is still marked when the low moon is seen across a featureless sea horizon.

Helen Ross and Cornelis Plug have carried out their research extremely well. All the proposed explanations are dealt with, and it is fair to say that most of them have fatal or near-fatal weaknesses; in fact, no single theory will suffice, and the whole problem is much more complex than might be thought.

For instance, it has been suggested that dustiness in the lower atmosphere, near the horizon, might blur the moon's edges and enlarge the disc, but simple measurements are enough to show that this is not so. Colour may play a part, and of course the low moon may appear orange or red because of the absorption in our atmosphere, but the effect on the apparent size of the disc is minor. (Incidentally, there is a similar "sun illusion" - much less well known because it is unwise to look straight at the sun even when it is setting and seems to be mild and harmless.) Then there is the question of the estimated distance; does the low moon seem to be nearer or further away than the high moon?

It is easy to measure the real size that an object presents, but it is much more difficult to measure the apparent size of an object. This is relevant to the whole problem. Various "moon machines" have been devised, and have given interesting results. One experiment - not included here - was made by Richard Gregory, who is a leading expert in the field and who wrote the foreword to this book. In his experiment (in which I took part) we waited until nightfall and fixed up a movable mirror so that the apparent size of the real moon could be compared with that of an artificial moon some yards away. Using an iris, the size of the artificial moon could be altered, and by swinging the mirror it was possible to alter the apparent altitude of the image of the real moon. First the real moon was brought down "side by side" with the artificial one, and the iris adjusted until the two disks of light appeared equal. Then the real moon was raised - and it seemed to shrink, so that the artificial image had to be reduced by at least 10 per cent before the two again appeared equal. Therefore, what was being measured was the apparent size. Various similar experiments are described in the book, and the results are very interesting indeed.

The text has been meticulously researched, and the only real mistake found is on page 13, where the moon's orbital period (.3 days) is confused with its synodic period (29.5 days, the interval between one full moon and the next). The authors' style is clear, making the book accessible to newcomers, and the illustrations are excellent.

There can be no doubt that this book will remain the standard work in the subject, and it will appeal to readers of all types. Yet, despite all the effort that has gone into it, no clear-cut answer is forthcoming and there must be many contributory factors. We do not yet have a full understanding of the moon illusion.

Sir Patrick Moore is the author of more than 60 books, mainly on astronomy.